Format of Original
American Mathematical Society
Proceedings of the American Mathematical Society
Original Item ID
doi: 10.1090/S0002-9939-1983-0715874-4; Shelves: QA1 .A5215 Storage S
We answer some questions raised in . In particular, we prove: (i) Let F be a compact subset of the euclidean plane E2 such that no component of F separates E2. Then E2\F can be partitioned into simple closed curves iff F is nonempty and connected. (ii) Let F Ç E2 be any subset which is not dense in E2, and let S be a partition of E2\F into simple closed curves. Then S has the cardinality of the continuum. We also discuss an application of (i) above to the existence of flows in the plane.
Bankston, Paul, "On Partitions of Plane Sets into Simple Closed Curves II" (1983). Mathematics, Statistics and Computer Science Faculty Research and Publications. 130.